How to Find the Greatest Common Factor

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Finding the greatest common factor (GCF) [1] of a number set can be easy, but there are several steps you'll need to follow to get there. In order to find the greatest common factor of two numbers, you'll need to factor out both of those numbers using your knowledge of timetables, then identify the largest number that appears in both sets of factors.

Method 1
Method 1 of 2:

Comparing Common Factors

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    You don't have to know prime factorization to find the greatest common factor. Start by finding all the factors of the set you are comparing. [2]
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Method 2
Method 2 of 2:

Using Prime Numbers

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    Factor each number completely into its prime numbers. [3] A prime number is number greater than 1 that has no factors but itself. Examples of prime numbers include 5, 17, 97, and 331, to name just a few.
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    [4] Pick out any prime numbers between the set that are the same. There can be several common factors, one common factor, or none.
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    If there are no common factors then the greatest common factor is 1. If there's only one prime common factor, then that's your common factor. If there are multiple prime common factors, then multiply all the prime common factors together to get your greatest common factor [5] .
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  • Question
    What's the greatest common factor of 4x^3y, 8x^2y^3, xy^3z^5?
    Donagan
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    The three terms are: 4x³y, 8x²y³, and xy³z^5. First, in terms of numerical coefficients, the lowest coefficient in the three terms is 1. The lowest x exponent is 1. The lowest y exponent is also 1. There is no z in two of the terms (so z is not a common factor). That means the greatest common factor among the three terms is 1xy (or xy).
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  • Question
    What is the use of prime numbers in our lives?
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    The average person is never likely to use prime numbers. They do have certain applications within science and mathematics.
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      • Did you know that the mathematician Euclid of the third century B.C.E. created an algorithm for finding out what the greatest common factor is in the case of two natural numbers or two polynomials? [6]
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      References

      1. ↑ https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-greatest-common-divisor/v/greatest-common-divisor
      2. ↑ https://www.mathsisfun.com/numbers/factors-all-tool.html
      3. ↑ https://mathworld.wolfram.com/PrimeNumber.html
      4. ↑ https://www.mathsisfun.com/prime-factorization.html
      5. ↑ https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/a/factoring-by-grouping
      6. ↑ https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm

      About This Article

      Article Summary X

      To find the greatest common factor of two or more numbers, make a list of all of the factors of each number. For example, for the number 10, the factors are 1, 2, 5, and 10, and for the number 21, the factors are 1, 3, 7, and 21. Then, compare the list of factors to find the largest number that the two have in common. For 10 and 21, the greatest common factor is 1. To learn more, like how to use prime numbers to find the greatest common factor, keep reading!

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